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Understanding Lucky Dough Chances

  • The Lucky Dough game consists of a square with nine boxes.
  • The player selects a number from 1 to 5 in each of the eight boxes; the center box is always a free match.
  • The more lines a player matches, the bigger the prize.

You Can Calculate the Odds of Winning Lucky Dough.

To calculate the odds of winning the game, here are a few terms you'll need to know:

F = Field Size, or the number of numbers that can be drawn in any box. In this case, it is always 5.
N = Number of Fields
, or the number of boxes in the game. It's always 8 in this game, since the center box is
      always a free match.
M = Number of Fields Not Matched, or missed fields.
P = Number of Permutations, or possible outcomes that can result from a drawing.
C = Combinations that form a line.

^ = Symbol representing an exponential; directs us to raise that number to the nth power.
      For example, 3^ means 3 x 3 x 3, or 3 to the 3rd power.
* = Symbol representing multiplication.
      For example, 3*3 means 3 multiplied by 3.
/ = Symbol representing division.

So, let's get started.

The basic formula for calculating the odds of winning in a combinatorial line game looks like this:

(((F-1)^M)*P) / (F^N)

For any prize level, say three lines, there are numerous combinations of outcomes that can form a line. For example, 14 ways to match in 6 of 8 boxes and form 3 winning lines and 16 ways to match 5 of 8 boxes and form 3 winning lines. When there are numerous combinations possible, they are added together in the numerator of the probability formula.

Let's work through an example.

It may look hard, but it really isn't. We can find the odds of winning 3 lines by plugging the numbers into the formula above. It looks like this:

(((5-1)^2)*14+((5-1)^3)*16) / (5^8)

((4^2*14)+(4^3*16)) / 5*8
(4 squared times 14 plus 4 cubed times 16 divided by 5 to the eighth power)

((16 times 14) plus (64 times 16)) divided by 390,625

224 plus 1024 divided by 390,625

1248 divided by 390,625


The odds of winning are 1/.003195

or 313 to 1

You can calculate the odds for other outcomes using this example as your guide.

For any questions regarding the above information, please feel free to contact our Research & Development Division.

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